Dynamic wind turbine wake reconstruction: A Koopman-linear flow estimator

Abstract

A challenging topic arising in dynamic wind turbine wake is modeling, especially the low-order approximation. The central problem is the fact that it has high-dimensional and nonlinear wake characteristics. In this paper, a Koopman-linear flow estimator is designed according to the Koopman operator theory. Different from the conventional flow reconstruction with the linear stochastic estimation method, a dynamic state-space model with physical states is constructed. The wake dynamics are approximated using a limited number of measurable physical parameters by the dynamic part; then, the full wake flow is reconstructed from the low-order states by the estimation part. The flow estimator is designed into three different forms following Extended Dynamic Mode Decomposition (EDMD) method. Each form has its unique advantages. Precisely, probe sensors are placed in the studied space and provide direct information of the wake, and a few in-directly physical parameters are also included. Nonlinear integer programming is further adopted using a heuristic optimization algorithm, by which the sensor configurations are optimized. Comparisons with the standard Dynamic Mode Decomposition (DMD)-based wake model are adopted in time domain and frequency domain to verify the effectiveness of the proposed flow estimators. The results show acceptable accuracy in typical modeling cases and maintain good estimation accuracy when the measurement noises are involved. Finally, the proposed Koopman-linear flow estimator is compared with related stochastic estimation methods, in which the connections of the proposed estimator with stochastic ones are also discussed.